Final answer:
To find the tension in the lower rope, use Newton's second law and draw a free-body diagram to equate the sum of the rope tensions to the weight of the object, solving for the unknown tension. The correct option is A.
Step-by-step explanation:
To find the tension t2 in the lower rope for a situation where objects are at rest or moving at a constant velocity, we can apply Newton's second law of motion. According to this law, if an object is in static equilibrium (not accelerating), then the net force acting on it must be zero. This principle allows us to set up equations that balance the tension forces against the weight of the object.
First, draw a free-body diagram showing all the forces acting on the object. This diagram will include the weight of the object (due to gravity) acting downwards and the tensions in the ropes acting upwards. The balancing of forces in the vertical direction can be expressed as ∑Fy = 0, where Fy is the vertical component of the forces.
Let's assume we know the tension in one of the ropes, T. The weight of the object also can be calculated as w = mg, where m is the mass of the object and g is the acceleration due to gravity (9.8 m/s²). If we have two ropes supporting the object, and the object is stationary, the sum of the tensions in both ropes must equal the weight. Thus, if T1 is the tension in one rope, and T2 is the tension in the second rope, we have T1 + T2 = w.
Using these principles, we can solve for T2 if the value of T1 and the weight w are known.